A large tank contains two immiscible liquids that form a sharp horizontal interface: a 0.40m-deep layer of fresh water (density 1.0×103kgm−3) floats on top of a much deeper layer of liquid metal alloy whose density is 7.0×103kgm−3. A solid block shaped as a cube with edge length 0.10m and density 2.0×103kgm−3 is released from rest at the center of the tank and is allowed to reach static equilibrium.
(a) After equilibrium is reached, the cube straddles the interface so that its top face is flush with the water surface. Derive an expression for, and then calculate, the fraction of the cube’s volume that is submerged in the lower liquid metal alloy.
(b) The cube is now pushed entirely into the metal alloy so that no part of it contacts the water layer and is again released from rest. Predict whether the cube rises back to the interface, sinks deeper into the alloy, or remains where released. Justify quantitatively.
(c) Suppose instead that the lower liquid is replaced by kerosene (density 8.1×102kgm−3) while the upper water layer remains. Without performing additional calculations, explain qualitatively where the cube will come to rest relative to the new interface and the water surface.